Convex side of a thin concavo-convex lens(μ=1.50) has a radius of curvature of 20cm. The concave surface has a radius of curvature 60cm. The concave part is filled with water of μ=1.33 and the convex side is silvered. What is the effective focal length of the optical system?

Dear Abhipsa,

We know the lens makers formula...

Now the given case can be considered as combination of

1. A thin lens of Radius of curvatures given by R₁= infinity and R₂= -60 cm

and μ = 1.33 refractive index of water

it is a thin lens

thus focal length of this lens is f₁= 181.81 cm.

2. A concavo convexlength of  R₁= -60 and R₂= -20 cm

and  μ = 1.5

thus focal length of it for the case of thin lens is f₂=60 cm

and

3. A concave mirror of focal length f₃= -R/2 = -10 cm

where R= 20cm

thus resultant focal length becomes 1/f = 1/f₁ + 1/f₂ + 1/f₃

 as distances between the lenses are zero

thus resultant focal length is -12.85 cm.

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